TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}^+\cr \cr f(w) &=& \dfrac{w - 13}{- 8 \sqrt{w}}\cr \cr \quad u(w) &=& w - 13 & \Rightarrow & u'(w) &=&1\cr \quad v(w) &=&- 8 \sqrt{w} = -8w^{\frac{1}{2}} & \Rightarrow & v'(w) &=& -8\cdot\dfrac{1}{2}w^{-\frac{1}{2}} = - \dfrac{4}{\sqrt{w}} \cr \cr f'(w) &=& \dfrac{1\cdot \left(- 8 \sqrt{w}\right)-\left(w - 13 \right)\cdot \left(- \dfrac{4}{\sqrt{w}}\right)}{\left(- 8 \sqrt{w}\right)^2} \cr \cr &=& \dfrac{-\dfrac{8w}{\sqrt{w}}+\dfrac{4w - 52}{\sqrt{w}}}{64 w} \cr \cr &=& \dfrac{\dfrac{-4 w - 52}{\sqrt{w}}}{64 w} \cr \cr &=& -\dfrac{4(w +13)}{\sqrt{w}}\cdot\dfrac{1}{64 w} \cr \cr &=& - \dfrac{w + 13}{16 \sqrt{w^3}}\end{array}